Leisurely opening. I researched every single worker technology, then writing, and still had time to swing back to oracle Code of Laws. I even managed to spread Confucianism to my neighbor.
Since I ended up running a lot of cottages in my second city, I decided to move the palace there and build the Great Library in the old capital, which had plenty of food and production—the former to run scientists, and the latter to build the GL and National Epic.
In the first save, I am about to generate a great person, most likely a great scientist. This will be my fourth great person. I generated a scientist early, and then (unfortunately) a great prophet, and I researched music after literature and currency, getting the great artist.
Assuming that I get a scientist, here is the plan: bulb philosophy, use the great artist to generate a golden age, switch into caste/pacifism and churn out an obnoxious number of great scientists for heavy bulbing towards Liberalism. I love scientists so much that I will postpone bureaucracy until I can swap civics again. (effectively I am trading three turns of bureaucracy for two turns of caste/pacifism—I think it's worth it!)
This lets us hit Liberalism at 300 AD if we want... but more importantly, reducing the research time frees us to get the maximum possible beaker value out of it. There are plenty of options. Our AI friends are no help, unfortunately, so we'll have to research all the good stuff ourselves.
Here was my eventual choice, with the help of a chemistry double-bulb:
Next stop is Economics for the free great merchant. The Temple of Artemis is on our continent so we can make a quick buck.
Mehmed declares war at some point, putting me in the awkward position of needing to revolt and 3-pop whip an unpromoted longbow. I should have been slightly more careful. But his units are hopelessly outdated. After he suicides his stack (almost taking a city!) I buy peace with Music.
I built any wonders that we had the resource for. (except the Hagia Sophia...) This may not have always been a good idea, but I never get any wonders on immortal so I had to indulge myself.
In 1080 AD I get my failure gold from the pyramids!
Second save I've just finished the Taj Mahal, and I have 12 turns of golden age ahead of me. I'll use this opportunity to bulb towards Biology and Electricity. (this is completely overkill and I'd never do it on immortal, but tanks are fun!) I'm also starting to build up heavy infrastructure in preparation for factories. At this point the deity players are shaking their heads at the slowness and inefficiency of my game.
My research is slowed down a whole bunch because I completely forget to send some galleons out at astronomy. Oh well. I lose the “world is round bonus” for this reason as well.
Other mistakes: because I skipped rifling, Mehmed declares again and manages to take Seattle with engineering units. Fortunately, I can use the Apostolic Palace to make peace and re-assign the city:
He'll pay, though.
The American unique unit actually sees some use:
Who needs siege when you're several eras ahead of your opponents?
I have many spare units during the war, and suffer virtually no casualties, so I go ahead and declare on Pericles so my SEALs have something to do while the tanks are on the way. A few turns later, I go ahead and declare on Suryavarman as well.
The most notable of moment of the war is when Mehmed suicides his entire stack against a city with a single SEAL for garrison.
The 1780 save is the last turn of the war. All three of our neighbors are dead. We have 33 cities (about to be 34 with the southern Barbarian city) and in 5 turns we can make ICBMs. Mining Inc is providing 18 hammers per city.
The 1820 save is where things get serious. We're about to buy peace between the Shaka/Ragnar empire and Mansa, then launch 25 ICBMs at Mansa's land.
After capitulation, we were still a half a percent short of domination, but throwing down a couple more cities solves that.
Note: I actually built a lot of malls in this game as well.